# Weak Convergence of the Sequence of Successive Approximations for Para--nonexpansive Mappings

@article{Yadav1980WeakCO, title={Weak Convergence of the Sequence of Successive Approximations for Para--nonexpansive Mappings}, author={B. S. Yadav and D. S. Jaggi}, journal={Publications De L'institut Mathematique}, year={1980}, pages={89-93} }

In a recent paper [4] F. E. Browder and W. V. Petryshyn have shown that if a nonexpansive mapping T: X—>X of a Hubert space X into itself is asymptotically regular and has a t least one fixed point then, for any x in X, a weak limit of a weakly convergent subsequence of the sequence of successive approximations {Tx} is a fixed point of T. The main object of the present note is to strengthen considerably this result by showing that under the same assumptions the sequence {Tx} is necessarily… Expand

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